intermediate value theorem for derivatives
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Darboux's_theorem
|
| gptkbp:appliesTo |
derivatives of real functions
|
| gptkbp:category |
theorems in calculus
|
| gptkbp:compatibleWith |
derivative to be continuous
|
| gptkbp:field |
calculus
real analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
intermediate value theorem for derivatives
|
| gptkbp:implies |
derivatives have the intermediate value property
|
| gptkbp:namedAfter |
gptkb:Jean_Gaston_Darboux
|
| gptkbp:publicationYear |
1875
|
| gptkbp:publishedIn |
gptkb:Annales_scientifiques_de_l'École_Normale_Supérieure
|
| gptkbp:relatedTo |
gptkb:Rolle's_theorem
mean value theorem intermediate value theorem |
| gptkbp:state |
If f is differentiable on [a, b], and if f'(a) < k < f'(b), then there exists c in (a, b) such that f'(c) = k.
|
| gptkbp:bfsParent |
gptkb:Darboux's_theorem
|
| gptkbp:bfsLayer |
7
|